\documentclass[12pt]{article}
\usepackage{amsmath, amssymb, graphicx, array, fancyhdr, unicode-math, multirow}

\DeclareMathOperator{\Var}{Var}
\DeclareMathOperator{\sd}{SD}
\DeclareMathOperator{\Pois}{Pois}
\DeclareMathOperator{\Bin}{Bin}
\DeclareMathOperator{\NegBin}{NegBin}
\DeclareMathOperator{\sech}{sech}


% Text: Calibri, all bold
\setmainfont{Calibri}
\renewcommand{\seriesdefault}{b}

% Math: choose a math font and visually embolden it
\setmathfont{TeX Gyre Termes Math}                  % base math font
\setmathfont[FakeBold=1.9]{TeX Gyre Termes Math}    % embolden; adjust 1.6–2.4

% header
\pagestyle{fancy}
\fancyhf{}
\lhead{\resizebox{!}{2cm}{M}}
\chead{\raisebox{0.5cm}{\Huge Posterior Probablities}} % (add title text if you want)
\rhead{\resizebox{!}{2cm}{M}}
\setlength{\headheight}{2.5cm}
\setlength{\headsep}{12pt} % space between header and body

\begin{document}
\thispagestyle{fancy}

% -------- PAGE 1 --------
\begin{table}[h!]
  \renewcommand{\arraystretch}{1.2}

  % -------- Single -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/single.png}}} 
&$ P(H) = 0.30 $\\
&$ P(L) = 0.70 $\\
&$ P(A|H) = 0.40 $\\
&$ P(A|L) = 0.20 $\\
&\\
\end{tabular}


% -------- Abstract -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/abstract.png}}} 
&$ P(A) = P(A|H)P(H) + P(A|L)P(L)$\\ 
&$ P(A) = (0.4)(0.3) + (0.2)(0.7) = 0.12 + 0.14 = 0.26   $\\
&\hrule\\
&\\
&$ P(H|A) = \frac{P(A|H)P(H)}{P(A)} = \frac{(0.4)(0.3)}{0.26} = \frac{0.12}{0.26} = \frac{6}{13} \approx 0.4615$\\
&\\
\end{tabular}


% -------- Question -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/question.png}}} 
&$P(R) = 0.70$\\
&$P(R^C) = 0.30 $\\
&$P(F|R) = 0.60$\\ 
&$P(F|R^C) = 0.10 $\\
&$P(R|F) = ? $\\
\end{tabular}
\end{table}
% second page
\newpage
\thispagestyle{fancy}
\begin{table}[h!]
% -------- Answer -------------------
\begin{tabular}{m{1.2in} m{4in}}
\multirow{5}{*}{\fbox{\includegraphics[width=1in]{images/key.png}}} 
&$P(R) = 0.70$\\
&$P(R^C) = 0.30 $\\
&$P(F|R) = 0.60$\\ 
&$P(F|R^C) = 0.10 $\\
&$P(R|F) = ? $\\
&\hrule\\
&\\
&$P(F) = P(F|R)P(R) + P(F|R^C)P(R^C)$ \\
&$= (0.60)(0.70) + (0.10)(0.30)$\\
&$= 0.45$\\
&\hrule\\
&\\
&$ P(R|F)  = \frac{ P(F|R) P(R)}{P(F)}= \frac{(0.45)(0.70)}{0.45} = 0.93$\\

\end{tabular}
\end{table}





\end{document}